The Controllability Principle in Responsibility Accounting
Rick Antle; Joel S. Demski
The Accounting Review, Vol. 63, No. 4. (Oct., 1988), pp. 700-718.
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Fri Apr 13 17:35:39 2007
THEACCOUNTING REVLEW
Vol. LXIII, No. 4
Octobrr 1988
Frank H. Selto, Editor
The Controllability Principle in
Responsibility Accounting
Rick Antle and Joel S. Demski
ABSTRACT: The purpose of this paper is to examine controllability: the notion a manager
should be evaluated based on that which she or he controls. We embed the managerial evaluation problem in a principal-agent setting and ask whether the optimal agency solution bears
any logical relation to a casual definition of controllability. It does not. More to the point, the
agency framework compels us to look at information content. This information content perspective, upon reflection, agrees with our intuition, with our anecdotal impressions of practice, and with the dictates of the principal-agent model. Moreover, there is a well-defined
relation between information content and a notion of control. Thus, the information content
perspective may be thought of as offering a precise definition of controllability.
a manager be evaluated as
the head of a cost center or a profit
and intuitive
center? Our
analysis of this perennial question f0cuses on whether the manager controls
cost and revenue. If so, the manager
should be evaluated as the head of a
profit center. If the manager only conirols cost, a cost center evaluation is
appropriate. If the manager only controls revenue, a revenue center evaluation is appropriate,
Analyzing this wisdom requires two
specifications. First, we must be precise
about what it means for the manager to
"control" cost or revenue. Second, we
must be precise about what it means to
evaluate the manager "correctly" or in
the "best possible manner."
We use a principal-agent model to
HOULD
Helpful comments of Froystein Gjesdal, Bob Kaplan,
Rick Lambert, KrishnaPalepu, FrankSelto, anonymous
reviewers, and seminar participants at Harvard Business
School, Mcblaster University, and Michigan State University as well as financial support from the National
Science Foundation are gratefully acknowledged.
Rick Antle and Joel S. Demski, Yale
University.
Manuscript received May 1986.
Revisions received March I987 and January 1988.
Accepted April 1988.
Editor's Note: In compliance with a resolution of the
Executive Committee of the American Accounting Association, no new manuscripts have been considered by
Education Research since June 30, 1987. Editor Frank
Selto indicates that this manuscript is the last to be published in Education Research. On behalf of the readers,
reviewers, and authors of Education Research, 1 wish to
thank Frank for his three years of exceptional service as
Editor of the section.
Antle and Demski
provide a coherent framework for the
evaluation exercise. This gives a setting
where a nontrivial control problem is
present, where evaluation of the manager can be explicitly modeled, and
where managerial evaluation can be endogenously specified. In this way a control problem is modeled as an exercise in
motivating a particular behavior by the
manager, and performance evaluation as
producing information relevant to the
question of whether the desired behavior
was supplied. The focus is on control of
inputs, not outputs. Managerial evaluation, then, becomes framed in terms of
inferring this supply of input.
In turn, we specify what it means for
the manager to "control" an evaluation
statistic, such as cost or revenue, by asking whether his or her supply of inputs is
able to affect the probability distribution
of the output statistic. For example, if
cost is characterized as a probability distribution, can the manager affect this
distribution by altering her or his managerial inputs?
This particular definition is highly
stylized, but expositionally convenient.
A result is that the principal-agent analysis leads to a focus related to, but distinct from, this notion of controllability.
In particular, the principal-agent analysis leads us to ask whether the manager
can affect the probability distribution of
the output statistic conditioned on whatever other information is present. The
intuition for this conclusion is best developed by beginning with a stylized notion
of controllability, and then refining it to
match the principal-agent conclusion. In
this way the principal-agent paradigm is
used to infer a formal definition of controllability. For exposition purposes, we
refer to the performance evaluation dictates of the principal-agent model as the
information content approach and the
casual controllability definition as the
(traditional) controllability approach. '
The paper is organized as follows: In
Section I we present three numerical examples that explore the traditional controllability notion in a principal-agent
setting. In Section I1 we introduce the information content perspective and use it
to explain the anomalies in the earlier
examples. In Section I11 we illustrate this
perspective with a brief analysis of
tournaments. Conclusions are offered in
Section IV.
Basic Model
Consider a setting where an individual, termed a principal, owns a production function that offers uncertain cash
flow prospects. Three items of cash flow
are identified: cash inflow from customers (revenue), cash outflow for materials and overhead (cost), and cash outflow to compensate the supplier of labor
(wage). The revenue and cost amounts
depend on which state of nature obtains
as well as whether labor supply is
"LOW" or "HIGH." There are three
equally likely states of nature. The possibilities are described in Table 1 (000
omitted).
The principal faces two options,
whether to input labor supply HIGH or
LOW. She is risk neutral and, therefore,
evaluates the options in terms of the expected value of the net profit they
promise. To complete the analysis, we
muse specify the labor cost, or wage.
Labor is supplied by a second individual, termed an agent (or manager).
Three characteristics of this second indiWe emphasize our particular controllability rhetoric
is designed to build intuition. Earlier authors, such as
Ferrara [1967], were not as narrow in their conception of
controllability. On the other hand, we use the formality
of the principal-agent paradigm to propose a precise
notion of controllability.
The Accounting Review, October 1988
TABLE1
REVENUE, COST, AND GROSSPROFIT
FOR EXAMPLE
1
State
SI
LOW Labor Supply:
s3
Revenue
Cost, exclusive of labor
Profit, exclusiveof labor cost
HIGH Labor Supply:
s2
Revenue
Cost, exclusive of labor
Profit, exclusiveof labor cost
vidual are important. First, he is strictly
risk averse, and values his wage compensation according to the expected
value of [wage]y2. In this way, both individuals are important in the production
process. The agent supplies labor, while
the risk neutral principal supplies risk
carrying capacity.
Second, labor supply by the agent is
personally costly. He prefers LOW to
HIGH. In fact, his preference for wage
(w) and labor supply ( 1 ) is given by
the additive function [w]"- V(l), with
V(L0W) =O and V(H1GH) =50. In this
way the suppiier of labor is not an indifferent automaton. He and the principal
are in conflict. She prefers HIGH, while
he prefers LOW, other things equal.3
Third, the agent is not being held captive. He is free to work for the principal,
or to work "elsewhere. " Working elsewhere nets the agent an expected utility of
250 utiles. (For example, it offers a wage
of (250)2, and V(*)=O.) The principal
must match this to secure the agent's
employment.
With these details in place, we can cal-
400
800
400
400
-
culate the cost of labor. If the agent is to
supply 1=LOW, he must face a wage,
denoted wL, such that [wL]y2 -0 r250.
Otherwise, he does better by working
elsewhere. This implies W L ~ ( 2 5 0 ) '
=62,508. Similarly, to provide 1=HIGH,
the principal must offer a wage, denoted
Risk is noxious to the agent and a matter of indifference to the principal. Efficiency dictates the principal
shoulder the risk. In this way we view the principal as a
loose caricature of a capital market.
More specifically, contrast the agent's thoughts about
receiving $500 for certain or flipping a fair coin where
with probability 1/2 he "wins" 1000 and with probability 1/2 he "wins" nothing:
Concavity of [ * I f iguarantees the agent will reject fair
gambles. He considers risk noxious. The principal, however, is indifferent between the two options:
+
5 0 0 = 1/2[1oo0] 1/2[0].
' The idea is the two individuals face some conflict in
the employment relationship. In a larger model this
might arise over human capital concerns, over taste for a
particular style of administration or set of products, or
whatever. The most straightforward way is to assume
some type of nonpecuniary cost befalls the agent. We
further model this in a separable manner, so the conflict
does not interact with the agent's wage. While unrealistic, this allows us to examine the controllability dictates
in a transparent setting.
Antle and Demski
WH, such that [wH]V2 -50 2250. This implies w ~(300)2
r =90,000a4
The principal, of course, will pay what
the "market demands." Combining
these labor cost calculations with the
earlier (gross) profit data, we conclude
with the following analysis of the principal's decision (000omitted).
Labor Supply
LOW
HIGH
-
E(Revenue)
Less E(Cost)
933.33'
466.676
933.33
433.33'
E(Gross profit)
Less Wage
466.67
62.50
500.00
90.00
E(Net profit)
404.17
410.00
--
Evaluation Context
To this point there is little interest in
evaluating the agent. The principal prefers labor supply HIGH, while the agent
prefers LOW. But we have implicitly assumed the agent, in exchange for appropriate compensation, supplies the agreed
upon amount. If this assumption is accurate, there is no interest in verifying the
agent's labor supply.
Now move to the opposite extreme
and assume the agent operates in his self
interest. Further assume only the realized cost (exclusive of labor payment)
and revenue are jointly observable and
verifiable. Thus, the contract with the
agent can call for payment as a function
of the gross profit, but not as a function
of the labor input actually supplied. The
actual labor input is not verifiable and,
therefore, not available as a basis for
contracting.
This final verifiability assumption is
important because it allows the agent
room to maneuver in exploiting the natural conflict between principal and agent.
In particular, suppose the principal offers a guaranteed wage of w, =90,000in
fi
exchange for supply of input HIGH. The
agent can supply HIGH, with a resulting
utility measure of [90,000] -50 =250
or supply LOW with a resulting utility
measure of [90,000Ifi-0 =300 >250. In
short, supply of HIGH under this compensation arrangement is not incentive
compatible.
Our original analysis, in other words,
does not provide a practicable resolution
of the labor contracting problem in this
setting of self interested behavior coupled with limited observability and verifiability. We seek labor input, but cannot verify its supply. Only labor output,
cost and revenue here, is observable and
verifiable. Thus, we use the output to
infer the input. We evaluate the agent, so
to speak, based on his output. In this
way output serves two roles: it is a source
of value in the production process and it
is a source of information for the control
problem of motivating the self interested
manager. This gets to the basic question:
how should we use the information provided by output; do we want to use cost,
revenue, or cost and revenue to evaluate
the manager?s The question is interesting
because the value and information components of the output are not coextensive. We cannot unambiguously infer the
one from the other.
It is efficient to compensate the agent with a constant
wage. Otherwise, his payment is at risk while risk is
noxious to him but not to the principal.
' (1/3)(800) +(2/3)(1000)=933.33.
(1/3)(400) +(2/3)(500) =466.67.
' (2/3)(400) +(1/3)(500)=433.33.
We sketch the story in terms of cost, revenue, or cost
and revenue to provide a caricature of an institutional
setting. The typical cost center setting would, however,
focus on cost and physical output, as with a flexible
budget. So the available information is perhaps better
framed in terms of cost, physical output, and revenue
rather than cost and revenue. The addition of an explicit
output descriptor, though, needlessly complicates our
setting. Similar comments apply to variances.
The Accounting Review, October 1988
a = HIGH
(1/3)
Cost =400
w4
Cost =400
w4
Cost =SO0
Wa
(113)
(113)
Cost =so0
- ws
Cost = 500
Wa
Cost=400
(113)
(113)
w4
elsewhere
-
Controllability Answer
Consider the controllability prescription. If an output statistic such as revenue is used in the agent's evaluation then
the agent should be able to control that
statistic. Return to the data in Table 1.
The revenue depends on which state nature supplies, but not the labor input.
Conversely, the cost depends on both the
state and labor. The agent, through conscious behavior, can influence the cost
probability or lottery. The revenue probability or lottery is totally independent of
what the agent does. We conclude, using
this notion of controllability, our particular agent is best evaluated as the head
of a cost center. He controls cost, but
not revenue.
Model's Answer
Now ask the agency model the same
question. First, suppose we observe only
the cost outcome. What is the best way
to contract for supply of HIGH? The
trick is to design the agent's decision tree
so his self interested behavior mirrors the
principal's wishes. Let w, denote the
- -
agent's wage if cost =400 is realized and
ws if cost =500 is realized. The agent's
decision tree is shown in Exhibit l. Goal
congruence demands the agent prefer
HIGH to the other options. Thus, we
must engineer the ugent's decision tree so
HIGH is preferred. This requires:
and
The first inequality forces HIGH to be as
good as "go elsewhere.. . ." The second
forces HIGH to be as good as LOW. In
this way self interest on the agent's part
leads to choice of HIGH. Goal congruence is a constraint in designing the control system. We design the system so the
preferred behavior is in the agent's self
interest.
But achieving goal congruence is only
part of the principal's problem. Another
concern is the cost of aligning the agent's
behavior. Naturally, the principal will
select the w4\wS combination that is
least expensive. With the principal risk
Antle and Demski
(113)
a = HIGH
/
*a
Profit =600
8,
Profit = 500
ws
Profit =400
*4
Profit = 500
9s
Profit =SOO
9s
(113)
a=LOW
(113)
(113)
\
Profit =400
elsewhere
.,
neutral, least expensive means least expected payment to the agent when he is
motivated to supply HIGH. The best
combination is, therefore, located by the
following program:
Min 2/3 w,+ 1/3 w s
w..W,
subject to
The solution is w 4= 122,500 and w s
=40,000. The principal's evaluation is
now:
Contrast this with use of revenue and
cost in the agent's evaluation. Recalling
This solution can be developed in the following intuitive fashion. Suppose only the first constraint is binding. This is the setting where we have to induce the
agent to work for the principal, without any concern for
3eiecting HIGH over LOW. With the principal risk
neutral intuition correctly suggests w 4 = ws=90,000.
But the second constraint is violated. Conversely,
using only the second constraint requires [ w , ] h- [ w 5 ] %
= 150. Minimizing the expected payment implies w,=O
and w4=22,500, which violates the first constraint. By
implication both constraints are binding. Solving two
equations in two unknowns provides [w4]"=350 and
[w,]" =200, or w e = 122,500 and ws=40,000.
Alternatively, let v 4 = [w4]" and v s = [w,]". Substituting, our program is
Min 2/3v:+ 1/3v:
v.,
V,
subject to
Labor Supply
LOW
E(Revenue)
Less E(Cost)
E(Gross profit)
Less E(Wage)
E(Net profit)
HIGH
-
-
933.33
466.67
933.33
433.33
466.67
62.5010
500.00
95.00L'
104.17
-
405.00
-
This is a quadratic objective function with linear constraints and can be analyzed with standard optimization
routines, such as LINDO.Alternatively, direct numerical methods using standard software packages, such as
Borland's Eureka, can be used.
l o The earlier solution of w,=w5=62,500 satisfies
both constraints because there is no lower labor supply
than LOW.
(2/3)(122,500)+(1/3)(40,000)=95,000.
The Accounting Review, October 1988
the data in Table 1, we see the possible
(gross) profit realizations are 400, 500,
and 600. Let C4 denote the agent's compensation if a profit of 400 is realized, P5
if a profit of 500 is realized, and so
on. The agent's decision tree is shown in
Exhibit 2. Engineering the agent's tree
requires
1/3[$4]
V2
+
+
1/3[tir6]y2 1 / 3 [ ~ 5 ] ~ - 5 0
2250,
and
+
1/3[C4] '/'+ 1/3[@6IV2 1/3[6'5] -50
r 1/3[C4]V2+2/3[@s]R-0.
The principal's program becomes
Min 1/3ii.4+1/3~6+1/3+5
h,",,",
subject to
1/3[C4]'/'+1/3[C6]y2+1/3[C~]V2-50
r 250
1/3[ii.4] '/' + 1/3[@6]'/'+ 1/3[*5]% -50
r 1/3[fi4]" +2/3[@5]''-0
fi4, * 5 , f5i16 2 0.
The solution is fi4=90,000, fi5= 50,625,
fi6 = 140,625.12 The principal's evaluation is now:
Labor Supply
LOW
E(Revenue)
Less E(Cost)
E(Gross profit)
Less E(Wage)
E(Net profit)
HIGH
-
-
933.33
933.33
433.33
466.67
-
-
466.67
500.00
62.50
404.17
-
93.7513
406.25
P
The principal is strictly better off
using cost and revenue, as opposed to
just cost, in the agent's evaluation. The
agent, however, is indifferent. In either
case his expected utility is 250. Revenue
is a useful evaluation statistic, despite
the controllability-based conclusion it is
not controllable and, therefore, useless
in the evaluation exercise. l 4
A Second Example
Now consider a slight variation on this
example. Everything is identical except
the revenue structure is altered in Table 2
(000omitted).
This makes the revenue lottery dependent on the agent's behavior. So a controllability approach would imply revenue is a useful evaluation statistic
because the agent is able to influence
which revenue result obtains. Further
observe the revenue structure is constructed so a cost realization of 400 always is accompanied by a revenue realization of 1000; and a cost realization of
5 0 0 always is accompanied by a revenue
realization of 800. l 5 Working through
" Sonir may be troubled by the non-monotonicity of
this contract, which calls for a higher payment to the
manager for achieving a profit of 400 than a profit of
500.Before concluding this does not accord with schemes
in practice, the following reinterpretation should be
considered. The manager's contract is equivalent to a
salary of 50,625, with a bonus of 39,375 for holding costs
to 400. 1f costs are "controlled" (i.e., held to 400) while
reveniie is "maintained" at 1000, the bonus is increased
to 90.000.
" Two important assumptions should be recalled.
First we carefully chose an illustration in which the relationship between revenue and cost and revenue less cost is
one to one. Otherkise, the precise pair of realizations is
important, not just their algebraic difference. Second,
we assume the principal is risk neutral. The agent, therefore, has no comparative advantage at carrying risk. If
this were not the case we would always prefer a profit
center evaluation simply because efficient risk sharing
would dictate rhe principal and agent each have income
at risk. Here, however, we focus exclusively on control
considerations in examining how best to evaluate the
agent. This is accomplished by neutralizing the demand
for risk sharing with the agent. See Demski [1976].
I' This extreme case of a one-to-one association between cost and revenue makes the analysis transparent,
but is not necessary for the point to hold. As is discussed
later, the important feature is that the distribution of
revenue conditional on cost does not vary with the
agent's behavior. The distinction is one of equivalence in
(conditional) distribution, not of "equality" in the guise
of a one-to-one association. Of course, the latter implies
the former.
Antle and Demski
TABLE
2
REVENUE, COST,AND GROSS
PROFITFOR EXAMPLE
2
State
Sa
LOW Labor Supply:
Revenue
Cost, exclusive of labor
Profit, exclusive of labor cost
HIGH Labor Supply:
Revenue
Cost, exclusive of labor
Profit, exclusive of labor cost
the details of the agency framework will
produce the following conclusions: (1)
the principal prefers to implement a
HIGH supply of labor; (2) the most efficient contracting arrangement is use of
the cost outcome, accompanied by w4
= 122,500 and ws=40,000; and (3) revenue is of no use in evaluating the
agent.16 Thus, we have a case where a
controllability focus implies revenue is
an important evaluation statistic while
an agency analysis implies it is superfluous.
A Third Example
For a final example, change the revenue structure in our setting as described
in Table 3 (000 omitted). As in the second example, revenue now depends on
the agent's behavior and a controllability
focus implies it is best to hold the agent
responsible for the cost and revenue (or
profit) outcomes. In turn, working
through the details of the agency framework reveals: (1) the principal prefers to
implement a HIGH supply of labor; and
(2) the most efficient contracting arrangement is use of cost and revenue
with payment to the agent of G=O when
loo01
400
S2
800
500
Sn
800
500
-
-
600
300
300
loo0
400
loo0
800
500
-.
400
-
-
600
600
-
-
300
-
a profit of 200 obtains and *=90,000
otherwise.
In this setting, a profit of 200 signals
unmistakably the agent has supplied
LOW. So the contract "penalizes" the
maximal amount by paying 0 (dismissal?). This threat allows for an equilibrium payment of 90,000. We, thus,
have an illustration where the controllability anti agency analyses agree.
These examples, taken together, give
settings wh~erea non-controllable item is
useful, where a controllable item is useless, and where a controllable item is
useful. The important question is what
explains this schism between the common sense of the controllability notion
and the deductive sense of the principalagent exercise. The answer is to be found
in the probabilities of the revenue and
cost outco~ne.
More precisely, knowledge of cost implies knowledge of revenue and vice versa. So using only cost, using
only revenue, or using cost and revenue are identical
evaluation schemes. Also notice HIGH is preferred here
because we have the same cost structure along with less
revenue prospects under LOW.
708
The Accounting Review, October 1988
State
LOW Labor Supply:
HIGH Labor Supply:
Revenue
Cost, exclusive of labor
SI
SI
s3
800
700
400
500
loo0
500
-
-
-
Profit, exclusive of labor cost
500
200
500
Revenue
Cost, exclusive of labor
800
400
1000
400
loo0
Profit, exclusive of labor cost
To develop this point, notice the common structure in the above examples
centers on two facts: First, there is inherent conflict because the principal wants
to implement one labor supply (HIGH)
while (other things equal) the agent
wants to implement a different labor
supply (LOW). Second, informational
asymmetry is present since the cost and
revenue outcomes do not necessarily reveal exactly what input the agent has
supplied. Put differently, the principal
seeks input from the agent, but cannot
directly observe input. As a result, the
parties contract on observable and verifiable output. In short, output is used as
an imperfect indicator of input, and the
information content of output becomes
of concern. ''
Information Content
Information content is a subtle notion
in this setting. We use the cost and revenue outcomes as indicators of what input
was supplied. In particular, we use the
statistical pattern of these outcomes. But
since we are concerned about the agent's
supply of input, we contrast the statisti-
400
-
500
-
-
600
500
-
-
cal pattern under the assumption he supplies the desired input with the statistical
pattern under the assumption he supplies
some other input.
To develop this theme, we contrast
two probability statements: (1) the probability of revenue=R under inputs a
=HIGH and a=LOW; and (2) the
probability revenue=R under inputs a
=HIGH and a=LOW conditioned on
cost = C. Let f (R 1 a) denote the probability revenue =R when the agent supplies input =a. Also, let f (R C,a) denote the probability revenue =R when
cost = C has been observed and when the
agent supplies input =a. These probabilities, for the three examples, are displayed in Table 4. l 8 Notice, in particular,
I
l7 As mentioned earlier, the productive output provides value (here in the sense of profit) and information.
In an extended setting, we would then design the productive process to balance these two types of output. As a
result, we d o not model the setting as one of finding the
least costly control system to implement the otherwise
most efficient productionarrangement. The design problem does not separate.
The easiest way to replicate these calculations is
to construct the joint probabilities, f (R,Cla). These
are displayed in the Appendix. By the laws of probability, we have f ( C i a )=f (7OO,Cla)+f (800,Cla)
+f(lOOO,Cla) andf ( RjC.a)=f(R,Cla)/f (Cla).
Antle and Demski
709
TABLE
4
MARGINAL AND CONDITIONAL
PROBABILITIES
--
----
Example I
Revenue
Revenue
800
a=LOW
a =HZGH
Cost
Cost
800
Revenue
1000
800
loo0
Example 2
f(Rla)
a=LOW a=HZGH
Revenue
800
loo0
f ( R I C,a)
Revenue
a=LOW
a =HZGH
Cost
cost
800
loo0
the following differences among the
three examples:
example one:
f ( R IHIGH) =f (R I LOW) and
f (RI C,HIGH) ff(RI CLOW)
example two:
f( R ( HIGH) #f (R1 LOW) and
f( R / C,HIGH) =f ( R I C,LOW)
Revenue
800
loo0
example three:
f (RI HIGH) #f (RI LOW) and
f (RI C,HIGH) #f (R I C,LOW). l9
IP Two other points should be noted. First, an example
where revenue is simply noise would provide a setting
with f ( R /HIGH)=f( R [LOW) and f (R /C,HIGH)
=f ( R / C,LOW). Second, there is nothing ~atholoaical
about the examples. The data for exampie 2, fo; instance, exhibit perfect correlation between cost and revenue. But as mentioned in footnote 15, this is done to keep
The Accounting Review, October 1988
710
Example 3
Revenue
Revenue
700
a=LOW
a =HIGH
Cost
cost
700
0
1/2
800
1
0
Revenue
400
500
700
0
0
800
1/2
0
loo0
1/2
1
Consider f (R I a), the marginal probability revenue =R under input supply a.
f (R I HIGH =f (R I LOW) in the first example, while f (R I HIGH) ff (R I LOW)
in the second and third examples. By
conscious choice of input, the agent controls the revenue probabilities (or revenue lottery) in the latter two examples,
but not in the first. This is the basis on
which we applied the controllability
notion.
definition: The agent controls revenue iff (R I a) is a nontrivial function of a.
the agent's compensation be denoted
w=I(R,C). If revenue of R and cost of
C are realized the agent is paid amount
w=I(R,C). If for some value of C different values of R lead to different payment amounts, we then say the agent is
held responsible for revenue.
definition : The agent is held responsible for revenue (cost) under I(R,C) if I(R,C) is a
nontrivial function of revenue (cost). 21
That is, we say the agent
nue if he is able to affect the marginal
probability of revenue through his behaviOr (i.e., his s l l ~ ~ labor
l ~
NOWconsider the use of revenue (or
cost) in the compensation arrangement.
We say the parties use the revenue measure if the agent's compensation depends
On the actual revenue realization. Let
the illustration uncluttered. Consider a setting where
revenue is either 1000 or 800. Let the revenue lottery
depend only on cost, and be such that R = 1000 is more
probable with one cost realization thananother. This will
ensure f(R I HIGH) ;tf (R 1 LOW) and f (R 1 C,HIGH)
=f (R I C,LOW). See the extended examplethat begins in
footnote 26.
~ n ~ ~ ~ can~be made
~ ~about
m controUing
e n t
21 BYnontrivial we mean for some value_of C, say_e,
we have distinct R1and R2suchthat I ( R L , C ) fI(R2,C).
Antle and Demski
From here we articulate the controllability notion as saying the agent should be
held responsible for revenue if he controls revenue, for cost if he controls cost,
and for profit if he controls revenue and
cost.22By this principle, the agent should
be held responsible for cost in each of
the three examples, and for revenue
(and, therefore, profit) in only the latter
content in terms of inferring what the
agent supplied. If this is the case, holding the agent responsible for revenue and
cost is inefficient. It merely "noises up"
the evaluation. Revenue variations are,
in the presence of cost, pure noise. This
suggests the following:
definition : Revenue has information
content in the presence of
cost i f f (R I C,a) is a nontrivial function of a.
Conditional Probabilities
The conclusion above does not agree
To understand this definition, suppose
with the principal-agent solutions, where we already know cost and focus on the
we find revenue a useful evaluation mea- conditional distribution of revenue,
sure in the first and third examples.24 f (R / C,a). If the agent cannot influence
This discrepancy arises because informa- this conditional distribution, we say revtion content and controllability are not
enue has no information content in the
coextensive. In the second example, for presence of cost. But if the agent can ininstance, the agent controls revenue, but
fluence this conditional distribution, we
revenue tells us nothing about the say revenue has information content in
agent's input, provided we already are the presence of cost. Note well, informaobserving cost. In this case, f (R 1 C,a) tion content is related to our concept of
depends only on cost; we may write control over revenue. The difference is
f (R I C,a) =f(R I C). Given we are al- we now acknowledge the information
ready using cost to evaluate the agent, content of cost. The focus is influence
the conditional probability of revenue, over the distribution of revenue given
f (R I C,a), cannot be influenced by the
agent.
Stated differently, the idea is the agent should be
In contrast, the agent does influence
held accountable for revenue if he controls revenue. Held
the conditional probability of revenue in accountable,
in turn, translates into I ( R , C ) is a nonthe other two examples. f (R IC,a) is a
trivial function of revenue in this setting.
l 3 Observe that the controllability principle can be
nontrivial function of input a in these
applied sequentially. If we are considering three varitwo cases. The explanation is, perhaps,
ables, say labor cost, raw material cost, and revenue, we
more clear if we factor the probability
can assess whether the manager controls each of these
variables without reference to theothers. In this way, one
construction:
22
f(R,Cla)=f(RlC,a)f(Cla).
If f (R I C,a) =f (R / C), we have a case
where the random variation in revenue
that is not explained by cost cannot be
influenced in any way by the agent's behavior. Stated differently, if f (R [ C,a)
=f (R 1 C) the random variation in revenue not explained by cost tells us nothing
whatever about whether the agent supplied a=LOW or a =HIGH. Given we
know cost, revenue has no information
form of textbook exercise consists of the specification of
the individual's position within the organization and a
list of potential performance measures. The student is
then asked to proceed down the list and suggest whether
each variable is controllable by the identified individual.
In this way, the student supposedly identifies the best
subset of variables for evaluating the individual in question.
24 More precisely, we are indifferent between use of
revenue or cost in the second example, but strictly prefer
use of both variables in the first and third examples. As
noted, the second example has a one to one relation between revenue and cost. An expanded version of the
example, as sketched in footnote 26, would have cost
strictly preferred to revenue, along with revenue being
useless in the presence of cost for evaluation purposes.
The Accounting Review, October 1988
cost is known. The key is f (R I C,a), not
content in the presence of cost, factoring
the probability provide^:^'
Model Interrogation
This shift in focus has intuitive appeal.
Marginal and conditional distributions
are not the same, and it seems we should
focus on what we learn conditioned on
what we are already observing. Moreover, the principal-agent analysis reinforces this intuition."
" Holmstrom [I9791 and Shave11 [I9791 developed the
generic argument that use of a monitor in the principalagent setting implies the monitor's conditional distribution is a nontrivial function of the agent's input. Subsequent studies, such as Baiman and Demski [1980],
Baiman [1982], and Demski and Sappington 119861, have
applied it to specific accounting questions. Baiman and
Noel [I9851 examine a multiperiod setting where noncontrollable capital cost is useful as a proxy for anticipated capacity choices by the principal when the agent is
induced to alter his input as a function of this proxy.
Further recall we assume the principal is risk neutral.
This means the agent is never used for risk sharing purposes. (By analogy, risk sharing is accomplished in the
capital, not the labor, market.) If the principal were also
risk averse here, simple risk sharing would dictate the
agent always be held responsible for revenue and cost,
since profit is at risk.
l6 To illustrate, consider a setting identical to that in
our earlier examples, except for the following relationship among states, acts, revenue, and cost (000 omitted):
f (R I a).
Claim: Suppose the agent is held responsible for revenue in the
optimal solution to the principal-agent problem. Then revenue has information content.
The assertion is nontrivial use of revenue (given cost is being used to evaluate
the manager) can only arise in the principal-agent solution if revenue has information content. To explore the formal reasoning, suppose, to the contrary,
we have a case where the agent is held
responsible for revenue even though
f (R I C,a) does not depend on input a. In
our specialized setting, this means we
have some Z(R,C) compensation scheme
that satisfies the following constraints: 26
and
The first constraint, recall, requires the
agent weakly prefer accepting the contract terms and supplying HIGH to his
other alternative, with a utility value of
8.The second requires the agent weakly
prefer accepting the contract terms and
supplying HIGH to accepting the contract terms and supplying LOW. Now,
since revenue does not have information
S,
S,
5,
2/16
1/16
2/16
LOW labor supply:
Revenue
Cost
Gross Profit
800
400
400
800
500
300
800
500
300
HfGH labor supply:
Revenue
Cost
Gross Profit
800 800 800 loo0 1000 I000 loo0
400400500400400400500
4004003WMX,600600500
probab~lity
S,
$4
S6
S,
1/16 6/16 2/16 2/16
800
500
300
1000
400
600
loo0
500
MO
1000
500
500
Further assume the agent is held responsible for revenue
and cost under the following I ( R , C ) payment arrangement:
1(1000,400)= 160,000,
I(l000,500)= 40,000,
1(800,400) = 40,000, and
1(800,500) = 10,000.
This payment arrangement meets the agent's required
utility constraint (of 250 utiles). It also induces the agent
to supply the HIGH labor input. Using the construction
that follows in the text, however, we can show this is a
wasteful arrangement because it ties the agent's pay to
revenue, which has no information content in the presence of cost. Subsequent notes trace this construction.
a' In the example in the previous footnote we have:
f (800,400 1 LOW) =f (800 1400,LOW)f (400 1 LOW)
=(.25)(.50) =.125,
f (800,400 /HIGH)=f (800 1400,HIGH)f (400 /HIGH)
= (.25)(.75) = .1875,
f (800,500 ILOW) =f (800 1500,LOW)f (500 /LOW)
=(.50)(.50) = .25, and
f (800,500 I HIGH) =f (800 1500,HIGH)f (500 /HIGH)
=(.50)(.25) = .125.
Note, f (800 /400,LOW) =f (800 1400,HIGH) = .25 and
Antle and Demski
With this factoring, we rewrite the constraints as follows:
~R.CI[I(R,C)I
'Y(R I C)Jf (CI HIGH)
V (HIGH) 2 0,
and
-
I
2 c d , c t [ ~ ( ~ ; c )(R
l ~ fC)l
-
f ( C I LOW) V(L0W).
Each term enclosed within the t o )
brackets is identical. This allows us to
express the constraints in the following
fashion:18
CC(CR[I(R,C)I'/'~
(R I C)lf (CIHIGH)
V (HIGH) r Q,
and
-
1 C)I
f (Cl LOW) - V(L0W).
From here we replace the common term
with a payment that depends only on
cost: l9
place I(R,C) with f(~).This replacement does not hold the agent responsible
for revenue, has lower expected cost to
the principal, delivers the same expected
utility to the agent, and induces the agent
to supply HIGHB30Put another way, the
f (c) construction is possible because we
are "filtering out" needless noise in the
evaluation process.
From Controllability to Information
Content
Thus, any solution that holds the agent
responsible for revenue when revenue
has no information content in the presence of cost can be improved. The key
f (800 /5OO,LOW)=f (800 1500,HIGH)= 3 0 . W e also
have f (10001LOW) = 10/16 and f (10001HIGH)
=11/16.
In the continuing example, these constraints become:
2 C,t~R[I(k,c)l'Y(R
f(C) is that payment the agent would
gladly exchange for the I(R,C) lottery.
Since the agent is held responsible for
revenue, we know <(R,C) is a nontrivial
function of R. But I(C) does not depend
on R. For each cost realization, tQeagent
is indifferent between receiving I(C) for
certain or engaging in the nontrivial
I(R,C) compensation lottery. But since
the agent is strictly risk averse, he is willing to pay a premium to unburden himself of this revenue risk:
In this way, the principal is able to re-
and
(400(3/4)+200(1/4)1(3/4)+ [200(1/2)+ 100(1/2))(1/4)
- 5 0 2 (400(3/4)+200(1/4))(1/2) [200(1/2)
100(1/2))(1/2)-0.
29 Continuing the example, we have the following constructions:
+
+
and
This is, in fact, theoptimal payment scheduleto motivate
choice of HIGH in this example. It has an expected labor
cost of 97,500. In contrast, the original I(R,C)arrangement has an expected labor cost of 103,750.
By construction we have:
z~,c[I(R'C)l'f (R,C I HIGH) - V(HIGH) r Zc[I(C)lSf(C1 HIGH) - V(H1GH)a U,
and
-
ZR,c[I(R,C)l'f (R,CI HIGH) V(HIGH)
r & [ f ( C ) l S f(CI HIGH) - V(HIGH)
h ER,cjII(R,C)lfif
( R 1C)If ( R (LOW)- V(LOW)
E Z , [ I ( ~ ) ] ~ ~ ~ ( C I L V(L0W).
OW)
-
The Accounting Review, October 1988
insight is we use the agent's output
(revenue and cost here) to infer his input.
This inferential exercise compares the
statistical properties of the agent's input
when he supplies the desired input with
those that arise when he supplies some
alternative input. Given cost is already
observed, an informative revenue output
means the (conditional) statistical properties differ according to the agent's
behavior. But an uninformative revenue
output means the (conditional) statistical
properties are independent of the agent's
behavior. Holding the agent responsible
for revenue in such a case has no effect
other than making his compensation
subject to purely random noise. In other
words, the information content of revenue is signaled by the conditional probability being controllable. Use of an
uninformative output statistic merely
subjects the agent to noise. The definition of information content tells us precisely when we would want to "filter
out" this noise in the agent's evaluation.
In this manner we conclude from the
principal-agent analysis that any use of
revenue in the agent's evaluation implies
revenue has information content in the
presence of cost. Conversely, with additional regularity assumptions (as in Holmstrom [I9821 or Demski and Sappington [1986]), we could provide a setting
where information content of revenue
necessarily implies the agent should be
heid responsibie for revenue. The important message, though, is no use of revenue is called for by the model unless revenue has information content in the
presence of cost.
The intuition for this conclusion parallels that for the original controllability
notion. The single variation in the logic
is to take account of what other information we already are observing. The key,
in other words, is to define controllability in terms of the conditional proba-
bility of the output statistic, thereby
taking account of the available information.
Stepping back from the examples and
analysis somewhat, we are focusing on a
setting where a list of performance variables is present and asking which elements on the list should be used in evaluating the manager (or agent) in question.
Applying the controllability notion, we
are led to a focus on marginal probabilities. Can the manager, through action,
control the probability distribution of
the variable in question. If so, the manager should be held responsible for that
variable. Control begets responsibility in
this framework.
Adopting a more explicit information
perspective, we ask what it is the manager is supposed to be doing and why we
want to evaluate his performance. Moving to an agency setting, the answers are
the manager is to supply personally
costly labor inputs, the supply of this
input is not observable, and we must use
output (including the output of various
performance statistics) as a noisy indicator of input. This allows us to be precise about the information content of an
evaluation measure. The key principle
turns out to be information content, a
close cousin of controllability but one
that adjusts for what other information
is already being used. Controllability
does not imply information content and
information content does not imply controllability.
Going still further, we now ask
whether this insight of distinguishing
controllability and information content
helps us solve or understand real problems as opposed to numerical examples.
This is not an easy task, because the information perspective demands we think
in terms of probabilities and take explicit
Antle and Demski
account of what other information is
being processed.
A ready illustration is provided by
tournaments. Familiar examples are
sports bonus clauses (e.g., for achieving
some type of all-star status) and sales
contests (e.g., sales person of the year
re~ognition).~'
Grading on a curve is a
common practice. Relative performance
evaluation of high level executives,
where compensation depends on performance relative to that of a peer (e.g.,
industry) group, is another illustration.
In each case a primary consideration in
the agent's evaluation is performance of
a peer agent. When viewed from a controllability perspective this is perplexing.
The agent in question has no control
over the performance of the peer. When
viewed from an information content perspective, this practice is far from perplexing. It is easy to imagine performance of another agent in similar
circumstances could possess information
content.32Each agent's performance is
affected by the common environment.
The peer's performance tells us something about that environment and, thus,
indirectly something about the performance of the agent in question.
Suppose two students take a common
examination. The second student's score
tells us nothing about the first student's
performance. But the second student's
score in conjunction with the first student's score typically does, by indirectly
telling us something about the common
environment. For the sake of argument,
suppose the score of student i is determined by
where effort, is the effort of the student
in question, noisei is randomness in the
examination environment that is idiosyncratic to our student, and instrument is
randomness associated with the exami-
nation instrument. Clearly, student i = 1
cannot control scorez. But score I
scorez is an interesting statistic, because
the instrument randomness has been factored out. In this way, scorez becomes
useful in the evaluation of student i= 1,
given we already know core^.^^
As another illustration, suppose we
have two agents, each working in the
environment described by Table 1. One
agent's output tells us something about
the state and, therefore, something
about the other's environment and, indirectly, something about the other's
input. In fact, agents working in perfectly correlated environments, an admitted extreme, is a case where one
agent's output is unusually informative
about the other agent, given we know
that agent's output.
-
IV. CONCLUSIONS
This paper offers a refined version of
the controllability principle. The argument rests on the assumption managerial
evaluation is aimed at producing information that reports on the managerial
services or inputs supplied. If the manager can affect the statistical pattern of
some particular variable, the manager
controls that variable. If the manager
can affect the statistical pattern condi-
'' Halberstam [1986]describes extensive use of sales
contests in the domestic automobile industry.
3' Baiman and Demski [1980]and Holmstrom [I9821
formalize this intuition in a principal-agent setting. Dye
[I9841 provides a general discussion of problems generated by tournaments. Antle and Smith 119861 provides
an empirical investigation, based on high level executive
compensation practices.
'' This vignette hints that an extension of our argument would have the agent's labor supply more generally
characterized in terms of quantity and quality. Alternatively, in this particular setting the student's performance would depend on effort, skill, and luck. We then
proceed as before, but in a manner aimed at information
content with respect to quantity and quality of input, as
opposed to quantity of input.
The Accounting Review, October 1988
tioned on whatever else we know, the
variable carries information content
about the manager's behavior. The concept of information content falls out of a
principal-agent analysis as being a central feature of valuable monitoring or
evaluation information. In this sense, we
offer the information content perspective as a refined version of the controllability principle. Whether the manager
controls the variable in question is
immaterial. Whether the manager controls (or influences) the variable in question, conditioned on whatever other information is present, is the key notion.
That is, information content is a precisely defined controllability notion that
accounts for other sources of information.
The darker side to this refined principle is the added demand it places on
the identification of a control problem.
With the traditional controllability notion, we need only ask whether the man-
ager can control the variable in question.
With the conditional or information
content notion, we must first specify
what other information is being used in
the evaluation process. Once this source
of information is accounted for, we ask
whether any new information is produced by the variable in question.34This
manifests itself in the manager's conditional control of the variable in question.
In short, we find the intuition of the
information content perspective appealing, but we also recognize assessing information content is likely to be a difficult task.
" Recent field studies by Merchant [I987 and Dent
[I9871illustrate this difficulty. Each study reports viola-
tions of the controllability principle. This is accomplished by documentation of various uncontrollable
phenomena that are used in the evaluation process. In
contrast, the information content perspective is not so
amenable to investigation. It demands assessing information content in light of all information beingused in
the evaluation process. The field investigator's task is
dramatically complicated by the importance of identifying the conditioninginformation.
Antle and Demski
Example 1
Revenue
a=LOW
a =HZGH
Cost
Cost
800
Revenue
800
loo0
loo0
Example 2
Revenue
800
1
a=LOW
a =HZGH
Cost
Cost
0
1
2/3
1
Revenue
800
loo0
Example 3
Revenue
a=LOW
a =HZGH
Cost
Cost
400
500
700
0
0
800
800
1/3
0
loo0
loo0
1 /3
1/3
700
Revenue
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The Accounting Review, October 1988
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[Footnotes]
14
Uncertainty and Evaluation Based on Controllable Performance
Joel S. Demski
Journal of Accounting Research, Vol. 14, No. 2. (Autumn, 1976), pp. 230-245.
Stable URL:
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25
Economically Optimal Performance Evaluation and Control Systems
Stanley Baiman; Joel S. Demski
Journal of Accounting Research, Vol. 18, Studies on Economic Consequences of Financial and
Managerial Accounting: Effects on Corporate Incentives and Decisions. (1980), pp. 184-220.
Stable URL:
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25
Line-Item Reporting, Factor Acquisition, and Subcontracting
Joel S. Demski; David E. M. Sappington
Journal of Accounting Research, Vol. 24, No. 2. (Autumn, 1986), pp. 250-269.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28198623%2924%3A2%3C250%3ALRFAAS%3E2.0.CO%3B2-A
25
Noncontrollable Costs and Responsibility Accounting
Stanley Baiman; James Noel
Journal of Accounting Research, Vol. 23, No. 2. (Autumn, 1985), pp. 486-501.
Stable URL:
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32
Economically Optimal Performance Evaluation and Control Systems
Stanley Baiman; Joel S. Demski
Journal of Accounting Research, Vol. 18, Studies on Economic Consequences of Financial and
Managerial Accounting: Effects on Corporate Incentives and Decisions. (1980), pp. 184-220.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%281980%2918%3C184%3AEOPEAC%3E2.0.CO%3B2-U
32
An Empirical Investigation of the Relative Performance Evaluation of Corporate Executives
Rick Antle; Abbie Smith
Journal of Accounting Research, Vol. 24, No. 1. (Spring, 1986), pp. 1-39.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28198621%2924%3A1%3C1%3AAEIOTR%3E2.0.CO%3B2-M
References
An Empirical Investigation of the Relative Performance Evaluation of Corporate Executives
Rick Antle; Abbie Smith
Journal of Accounting Research, Vol. 24, No. 1. (Spring, 1986), pp. 1-39.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28198621%2924%3A1%3C1%3AAEIOTR%3E2.0.CO%3B2-M
Economically Optimal Performance Evaluation and Control Systems
Stanley Baiman; Joel S. Demski
Journal of Accounting Research, Vol. 18, Studies on Economic Consequences of Financial and
Managerial Accounting: Effects on Corporate Incentives and Decisions. (1980), pp. 184-220.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%281980%2918%3C184%3AEOPEAC%3E2.0.CO%3B2-U
Noncontrollable Costs and Responsibility Accounting
Stanley Baiman; James Noel
Journal of Accounting Research, Vol. 23, No. 2. (Autumn, 1985), pp. 486-501.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28198523%2923%3A2%3C486%3ANCARA%3E2.0.CO%3B2-Z
NOTE: The reference numbering from the original has been maintained in this citation list.
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Uncertainty and Evaluation Based on Controllable Performance
Joel S. Demski
Journal of Accounting Research, Vol. 14, No. 2. (Autumn, 1976), pp. 230-245.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28197623%2914%3A2%3C230%3AUAEBOC%3E2.0.CO%3B2-K
Line-Item Reporting, Factor Acquisition, and Subcontracting
Joel S. Demski; David E. M. Sappington
Journal of Accounting Research, Vol. 24, No. 2. (Autumn, 1986), pp. 250-269.
Stable URL:
http://links.jstor.org/sici?sici=0021-8456%28198623%2924%3A2%3C250%3ALRFAAS%3E2.0.CO%3B2-A
NOTE: The reference numbering from the original has been maintained in this citation list.